There are also some new solid state type voltage limiters being sold, even some cheap one's on e-bay. I grabbed one of them, and it's been working great.
Sounds like you do have electrical problems, most likely the limiter or possible a break in the circuit board on the back. That can be repaired if you're handy. Just grab some thin copper plating, normally sold at hobby shops, and trim it with scissors and solder it over the break in the circuit.
And like stated above, if you've done all the electrical checks, make SURE you have a good float on your sending unit. I just went thru all that, just to find I had a float that had filled with gas. I emptied it out, soldered it shut again, and it's working great now.
You CAN remove the sending unit on the gas tank without dropping the tank on the '68s, you may be able to do it on your 66 as well. I'd check it out before you drop the tank. Just be ready for gas leakage cause anything over about 3/8ths a tank is gonna come pouring out of there when you start removing the sending unit.